ℒ Laplace Transform Calculator

🎯 Getting Started

This tool helps you work with Laplace Transforms, a powerful technique for solving differential equations.

• Forward Transform: Convert time-domain f(t) → s-domain F(s)
• Inverse Transform: Convert s-domain F(s) → time-domain f(t)
• Transform Table: Browse and search 30+ standard transforms

✏️ Input Notation

Time Domain (t):

• 1 - Unit step function
• t - Linear ramp
• t^n - Power functions
• e^(a*t) - Exponential
• sin(a*t), cos(a*t) - Trigonometric
• sinh(a*t), cosh(a*t) - Hyperbolic

S Domain (s):

• 1/s - Unit step
• 1/s^2 - Ramp
• a/(s^2 + a^2) - Sine
• s/(s^2 + a^2) - Cosine
• 1/(s-a) - Exponential

📚 Transform Table

Click any transform in the table to:

• View the complete transform pair
• See step-by-step derivation
• Copy to calculator instantly
• Understand the mathematical proof

🔢 Example Workflow

Solving a differential equation:

1. Take Laplace of both sides (use Forward mode)
2. Solve algebraically in s-domain
3. Use Inverse mode to get back to time domain
4. Reference table for complex terms